Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
Dr. Elisa Davoli, Università di Vienna
Sala conferenze IMATI-CNR, Pavia - Tuesday, December 18, 2018 h.15:00
Abstract. In this talk we establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid phase transitions in any arbitrary space dimensions, under a suitable anisotropic penalization of second variations. By means of Gamma-convergence, we show that, as the size of transition layers tend to zero, singularly perturbed two-well problems approach an effective sharp-interface model. The limiting energy is finite only for deformations which have the structure of a laminate. In this case, it is proportional to the size of the interfaces between the two phases.
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